The Flat Earth by Jefferson Bronfeld: Current Transformers and the Weird Parallel Anti-Universe

By Jefferson Bronfeld, Cadick Corporation

I don't know why you're afraid of falling off the edge. It is obvious to anyone who can see; the edge is where the earth meets the sky. The sky, being impenetrable, (I at least, have never penetrated it), will block you from traveling any further.

Sometimes our description of the edge is merely meant to help us explain the middle. This is especially true as we explore an often misunderstood power system device, the current transformer.

Current transformers are filled with mystery to a lot of us, and danger too. Connected to the secondary of a transformer you might expect a load, but no, in the case of current transformers you have a burden. And instead of opening the circuit to "kill" it, you keep the secondary circuit closed. In fact opening a current transformer secondary circuit could kill you, or at the very least cause a lot of damage.

It has been explained to me, and to you too perhaps, that since a current transformer (lets call it a CT) is meant to step down the current by the turns ratio, the voltage across an open secondary would be the power system voltage stepped up by the same ratio. So for example, a 1200:5 current transformer applied at 345 kV (199.2 kV phase to neutral) would have something like 48 million volts across its secondary if it were open.

This explanation is OK, especially if it impresses on people not to open a CT secondary. But the full explanation is much more interesting.

In my last column I talked about the source impedance, and its equally fictional friend, the infinite source. At the edge of our power system models we put an ideal voltage source behind a source impedance. The ideal voltage source is infinite in that the voltage stays rock solid regardless of how much current is drawn, which behavior would require infinite energy. The value of source impedance used in the model captures the actual voltage drop experienced with heavy current flow, and is, in fact, equal to the amount of voltage drop divided by the amount of current flow causing it.

You may remember from your circuit theory days the Thevenin equivalent source, which comes from Thevenin's Theorem. Thevenin said any combination of resistances and independent sources can be reduced to a single ideal voltage with a single equivalent impedance in series with it. The Thevenin equivalent source is equivalent to the original combination of resistances and sources; equivalent in that the two cannot be distinguished from one another by any voltage or current measurements made at their accessible terminals. They behave the same.

Well, just like Ralph Cramden, every Thevenin has his Norton. If you remember, Norton said any combination of resistances and independent sources can be reduced to a current source with an equivalent impedance in parallel with it. The Norton equivalent source similarly replicates all the behavior of the original circuit, and is equivalent, no surprise, to the Thevenin equivalent source for the circuit. Take the battery we talked about last time. We modeled it as a 12 volt ideal voltage source in series with a 0.1 ohm resistance. If, instead, we model it as a 120 amp ideal current source, with a 0.1 ohm resistor in parallel with it, we should get the exact same behavior, as measured externally. OK, I'll wait while you draw the circuit.

Let's see now, put a 1 ohm load resistor across the terminals. The 120 amps will divided between the internal resistance and external resistor, and using the good old current divider equation, (go ahead, look up the good old current divider equation), we get 10.9 amps through our load, just as before. And the voltage across the terminals? Well that comes out to 10.91 volts (120 amps times the parallel combination of 0.1 ohm and 1 ohm). Hmmmmm.

The Norton equivalent is another kind of edge to the power system model. Just like the ideal voltage source behind a source impedance (which we now know is a Thevenin equivalent) the Norton equivalent will behave just like the entire rest of the power system we did not wish to model explicitly. And like the Thevenin equivalent, it is made up of entirely fictitious elements. (By fictitious I mean the elements bare no correlation to any actual power system elements).

One of these elements, the more interesting one is the ideal current source. It is type of infinite source, this time providing the designated amount of current, (120 amps in our example above), regardless of the resistance it has to push through. And the terminal voltage will rise to what ever level it has to in trying to get this done. Did you get that? Stop and think about it. The current is not drawn from the circuit by the load, it is pushed into the circuit by the source. The current magnitude stays the same under all conditions, and the voltage is allowed to rise or fall as a consequence of the total parallel resistance (E=IR).

With our old ideal voltage source the voltage is fixed and the current magnitude is determined by the load. In an ideal current source, however, the current is fixed and the voltage is determined by the load. Its almost like we stepped into some weird parallel anti-universe. Let's see, exchange "current" for "voltage", "parallel" for "series"... I bet we can switch "open circuit" for "short circuit".

To get zero output from a voltage source, we open the circuit. To get zero output from a current source, we close it.

As we lower the resistance across a voltage source, the current flow increase. In the limit, as the resistance approaches zero, we get a theoretically infinite amount of current. (I=E/R and R=0). In reality if you short a voltage source you get one whopping huge amount of current until something is destroyed.

Well an analogous thing is true for current sources. As we raise the resistance across a current source the voltage increases. In the limit, as the resistance approaches infinity, we get a theoretically infinite amount of voltage. (E=IR and R=). In reality if you open a current source you get one whopping huge voltage until something is destroyed.

We are very accustomed to the voltage source way of looking at the (electrical) world. Where can we find an actual device that behaves like a current source? Check out our old friend the current transformer.

In a current transformer the power conducting lead (the overhead phase conductor or its connection to other equipment) makes up the primary winding. It is magnetically coupled with several turns of wire making up the secondary winding. We have a 1 to N transformer ratio, meaning we step down the primary current N times. In our 1200:5 CT discussed earlier we have a ratio of 1 to 240, meaning a primary current of 1200 amps will yield a secondary current of 5 amps.

Looking at the behavior of the secondary circuit, it can be thought of as a 5 amp ideal current source. 5 amps is pushed through the secondary circuit, through the "burden" impedance of all the relays and meters in the circuit. The voltage across the CT secondary will be what ever voltage is necessary to successfully jam that 5 amps into the circuit. You have all the energy of the interconnected power grid; all the generators on the continent, on the primary side of that current transformer. To the CT secondary it looks like... well, like an infinite source.

This explains why we are all the time calculating the burden, and trying to keep the burden low. If the burden is too high the secondary voltage will be too high and throw the CT into saturation.

Further, this explains why we don't want to open the CT secondary. An open in this circuit behaves as an infinite impedance. The interconnected power grid may not have infinite energy, but it will use what ever it has to jam 5 amps through that infinite impedance. The old unstoppable force against the unmovable object. The voltage on the CT secondary, (E=IR), will go screaming up as high as it can. At a high enough voltage the air gap across the circuit opening will break down and, and likely the circuit opening will flash over.

Stay tuned as I give more "round earth" explanations for various power system devices and phenomena often understood in a "flat earth" way. Until then, keep your CT secondaries shorted, and stay away from the edge.

Questions? Comments? Send them to editor@electricnet.com.

Jefferson Bronfeld is the Chief Engineer for Cadick Corporation, an electric power engineering consulting and training company. A licensed professional engineer with two patents, Jeff has over 19 years experience in the power industry. Jeff makes his home in Binghamton, NY, where, when not working, Jeff is active in the IEEE, and tutors mathematics to local junior high and high school students. When not being a nerd Jeff can be found playing fiddle tunes on the mandolin, fly fishing, or asking friends to take him sailing on their boat. Jeff's column appears every Monday on ElectricNet. (Back to top)